TSTP Solution File: COM013+4 by nanoCoP---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : COM013+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 10:14:32 EDT 2023
% Result : Theorem 1.64s 2.42s
% Output : Proof 1.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM013+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : nanocop.sh %s %d
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri May 19 03:12:36 EDT 2023
% 0.12/0.34 % CPUTime :
% 1.64/2.42
% 1.64/2.42 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.64/2.42 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.64/2.42 %-----------------------------------------------------
% 1.64/2.42 ncf(matrix, plain, [(579 ^ _86560) ^ [] : [-(aElement0(577 ^ []))], (581 ^ _86560) ^ [_105350] : [aElement0(_105350), iLess0(_105350, 577 ^ []), 589 ^ _86560 : [(590 ^ _86560) ^ [] : [-(aElement0(588 ^ [_105350]))], (609 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(_105350, xR, 588 ^ [_105350]))], (611 ^ _86560) ^ [_106402] : [aReductOfIn0(_106402, 588 ^ [_105350], xR)], (613 ^ _86560) ^ [] : [-(aNormalFormOfIn0(588 ^ [_105350], _105350, xR))], (592 ^ _86560) ^ [] : [-(_105350 = 588 ^ [_105350]), 595 ^ _86560 : [(607 ^ _86560) ^ [] : [-(sdtmndtplgtdt0(_105350, xR, 588 ^ [_105350]))], (596 ^ _86560) ^ [] : [-(aReductOfIn0(588 ^ [_105350], _105350, xR)), 600 ^ _86560 : [(601 ^ _86560) ^ [] : [-(aElement0(599 ^ [_105350]))], (603 ^ _86560) ^ [] : [-(aReductOfIn0(599 ^ [_105350], _105350, xR))], (605 ^ _86560) ^ [] : [-(sdtmndtplgtdt0(599 ^ [_105350], xR, 588 ^ [_105350]))]]]]]]], (642 ^ _86560) ^ [_107389] : [aNormalFormOfIn0(_107389, 577 ^ [], xR)], (615 ^ _86560) ^ [_106574] : [aElement0(_106574), -(aReductOfIn0(638 ^ [_106574], _106574, xR)), 620 ^ _86560 : [(621 ^ _86560) ^ [] : [577 ^ [] = _106574], (623 ^ _86560) ^ [] : [aReductOfIn0(_106574, 577 ^ [], xR)], (635 ^ _86560) ^ [] : [sdtmndtplgtdt0(577 ^ [], xR, _106574)], (637 ^ _86560) ^ [] : [sdtmndtasgtdt0(577 ^ [], xR, _106574)], (625 ^ _86560) ^ [_106932] : [aElement0(_106932), aReductOfIn0(_106932, 577 ^ [], xR), sdtmndtplgtdt0(_106932, xR, _106574)]]], (2 ^ _86560) ^ [_86684] : [-(_86684 = _86684)], (4 ^ _86560) ^ [_86791, _86793] : [_86793 = _86791, -(_86791 = _86793)], (10 ^ _86560) ^ [_86995, _86997, _86999] : [-(_86999 = _86995), _86999 = _86997, _86997 = _86995], (20 ^ _86560) ^ [_87308, _87310] : [-(isConfluent0(_87308)), _87310 = _87308, isConfluent0(_87310)], (30 ^ _86560) ^ [_87603, _87605] : [-(isLocallyConfluent0(_87603)), _87605 = _87603, isLocallyConfluent0(_87605)], (40 ^ _86560) ^ [_87898, _87900] : [-(aRewritingSystem0(_87898)), _87900 = _87898, aRewritingSystem0(_87900)], (50 ^ _86560) ^ [_88193, _88195] : [-(isTerminating0(_88193)), _88195 = _88193, isTerminating0(_88195)], (60 ^ _86560) ^ [_88516, _88518, _88520, _88522] : [-(iLess0(_88520, _88516)), iLess0(_88522, _88518), _88522 = _88520, _88518 = _88516], (74 ^ _86560) ^ [_88932, _88934] : [-(aElement0(_88932)), _88934 = _88932, aElement0(_88934)], (84 ^ _86560) ^ [_89283, _89285, _89287, _89289, _89291, _89293] : [-(sdtmndtplgtdt0(_89291, _89287, _89283)), sdtmndtplgtdt0(_89293, _89289, _89285), _89293 = _89291, _89289 = _89287, _89285 = _89283], (102 ^ _86560) ^ [_89892, _89894, _89896, _89898, _89900, _89902] : [-(sdtmndtasgtdt0(_89900, _89896, _89892)), sdtmndtasgtdt0(_89902, _89898, _89894), _89902 = _89900, _89898 = _89896, _89894 = _89892], (120 ^ _86560) ^ [_90501, _90503, _90505, _90507, _90509, _90511] : [-(aReductOfIn0(_90509, _90505, _90501)), aReductOfIn0(_90511, _90507, _90503), _90511 = _90509, _90507 = _90505, _90503 = _90501], (138 ^ _86560) ^ [_91090, _91092, _91094, _91096, _91098, _91100] : [-(aNormalFormOfIn0(_91098, _91094, _91090)), aNormalFormOfIn0(_91100, _91096, _91092), _91100 = _91098, _91096 = _91094, _91092 = _91090], (156 ^ _86560) ^ [_91653] : [aElement0(_91653), true___, -(true___)], (166 ^ _86560) ^ [_91908] : [aRewritingSystem0(_91908), true___, -(true___)], (176 ^ _86560) ^ [_92177, _92179] : [aElement0(_92179), aRewritingSystem0(_92177), 183 ^ _86560 : [(184 ^ _86560) ^ [_92399] : [aReductOfIn0(_92399, _92179, _92177), -(aElement0(_92399))]]], (190 ^ _86560) ^ [_92626, _92628] : [aElement0(_92628), aElement0(_92626), iLess0(_92628, _92626), true___, -(true___)], (208 ^ _86560) ^ [_93100, _93102, _93104] : [aElement0(_93104), aRewritingSystem0(_93102), aElement0(_93100), sdtmndtplgtdt0(_93104, _93102, _93100), true___, -(true___)], (230 ^ _86560) ^ [_93687, _93689, _93691] : [aElement0(_93691), aRewritingSystem0(_93689), aElement0(_93687), 241 ^ _86560 : [(242 ^ _86560) ^ [] : [sdtmndtplgtdt0(_93691, _93689, _93687), -(aReductOfIn0(_93687, _93691, _93689)), 250 ^ _86560 : [(251 ^ _86560) ^ [] : [-(aElement0(249 ^ [_93687, _93689, _93691]))], (253 ^ _86560) ^ [] : [-(aReductOfIn0(249 ^ [_93687, _93689, _93691], _93691, _93689))], (255 ^ _86560) ^ [] : [-(sdtmndtplgtdt0(249 ^ [_93687, _93689, _93691], _93689, _93687))]]], (257 ^ _86560) ^ [] : [-(sdtmndtplgtdt0(_93691, _93689, _93687)), 258 ^ _86560 : [(259 ^ _86560) ^ [] : [aReductOfIn0(_93687, _93691, _93689)], (261 ^ _86560) ^ [_94618] : [aElement0(_94618), aReductOfIn0(_94618, _93691, _93689), sdtmndtplgtdt0(_94618, _93689, _93687)]]]]], (273 ^ _86560) ^ [_95039, _95041, _95043, _95045] : [-(sdtmndtplgtdt0(_95045, _95043, _95039)), sdtmndtplgtdt0(_95045, _95043, _95041), sdtmndtplgtdt0(_95041, _95043, _95039), aElement0(_95045), aRewritingSystem0(_95043), aElement0(_95041), aElement0(_95039)], (299 ^ _86560) ^ [_95762, _95764, _95766] : [aElement0(_95766), aRewritingSystem0(_95764), aElement0(_95762), 310 ^ _86560 : [(321 ^ _86560) ^ [] : [322 ^ _86560 : [(323 ^ _86560) ^ [] : [_95766 = _95762], (325 ^ _86560) ^ [] : [sdtmndtplgtdt0(_95766, _95764, _95762)]], -(sdtmndtasgtdt0(_95766, _95764, _95762))], (311 ^ _86560) ^ [] : [sdtmndtasgtdt0(_95766, _95764, _95762), -(_95766 = _95762), -(sdtmndtplgtdt0(_95766, _95764, _95762))]]], (329 ^ _86560) ^ [_96620, _96622, _96624, _96626] : [-(sdtmndtasgtdt0(_96626, _96624, _96620)), sdtmndtasgtdt0(_96626, _96624, _96622), sdtmndtasgtdt0(_96622, _96624, _96620), aElement0(_96626), aRewritingSystem0(_96624), aElement0(_96622), aElement0(_96620)], (355 ^ _86560) ^ [_97315] : [aRewritingSystem0(_97315), 358 ^ _86560 : [(390 ^ _86560) ^ [] : [-(isConfluent0(_97315)), 394 ^ _86560 : [(395 ^ _86560) ^ [] : [-(aElement0(391 ^ [_97315]))], (397 ^ _86560) ^ [] : [-(aElement0(392 ^ [_97315]))], (399 ^ _86560) ^ [] : [-(aElement0(393 ^ [_97315]))], (401 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_97315], _97315, 392 ^ [_97315]))], (403 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(391 ^ [_97315], _97315, 393 ^ [_97315]))], (405 ^ _86560) ^ [_99195] : [aElement0(_99195), sdtmndtasgtdt0(392 ^ [_97315], _97315, _99195), sdtmndtasgtdt0(393 ^ [_97315], _97315, _99195)]]], (359 ^ _86560) ^ [] : [isConfluent0(_97315), 362 ^ _86560 : [(363 ^ _86560) ^ [_97633, _97635, _97637] : [383 ^ _86560 : [(384 ^ _86560) ^ [] : [-(aElement0(382 ^ [_97315, _97633, _97635, _97637]))], (386 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(_97635, _97315, 382 ^ [_97315, _97633, _97635, _97637]))], (388 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(_97633, _97315, 382 ^ [_97315, _97633, _97635, _97637]))]], aElement0(_97637), aElement0(_97635), aElement0(_97633), sdtmndtasgtdt0(_97637, _97315, _97635), sdtmndtasgtdt0(_97637, _97315, _97633)]]]]], (417 ^ _86560) ^ [_99568] : [aRewritingSystem0(_99568), 420 ^ _86560 : [(452 ^ _86560) ^ [] : [-(isLocallyConfluent0(_99568)), 456 ^ _86560 : [(457 ^ _86560) ^ [] : [-(aElement0(453 ^ [_99568]))], (459 ^ _86560) ^ [] : [-(aElement0(454 ^ [_99568]))], (461 ^ _86560) ^ [] : [-(aElement0(455 ^ [_99568]))], (463 ^ _86560) ^ [] : [-(aReductOfIn0(454 ^ [_99568], 453 ^ [_99568], _99568))], (465 ^ _86560) ^ [] : [-(aReductOfIn0(455 ^ [_99568], 453 ^ [_99568], _99568))], (467 ^ _86560) ^ [_101448] : [aElement0(_101448), sdtmndtasgtdt0(454 ^ [_99568], _99568, _101448), sdtmndtasgtdt0(455 ^ [_99568], _99568, _101448)]]], (421 ^ _86560) ^ [] : [isLocallyConfluent0(_99568), 424 ^ _86560 : [(425 ^ _86560) ^ [_99886, _99888, _99890] : [445 ^ _86560 : [(446 ^ _86560) ^ [] : [-(aElement0(444 ^ [_99568, _99886, _99888, _99890]))], (448 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(_99888, _99568, 444 ^ [_99568, _99886, _99888, _99890]))], (450 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(_99886, _99568, 444 ^ [_99568, _99886, _99888, _99890]))]], aElement0(_99890), aElement0(_99888), aElement0(_99886), aReductOfIn0(_99888, _99890, _99568), aReductOfIn0(_99886, _99890, _99568)]]]]], (479 ^ _86560) ^ [_101821] : [aRewritingSystem0(_101821), 482 ^ _86560 : [(501 ^ _86560) ^ [] : [504 ^ _86560 : [(505 ^ _86560) ^ [] : [-(aElement0(502 ^ [_101821]))], (507 ^ _86560) ^ [] : [-(aElement0(503 ^ [_101821]))], (509 ^ _86560) ^ [] : [-(sdtmndtplgtdt0(502 ^ [_101821], _101821, 503 ^ [_101821]))], (511 ^ _86560) ^ [] : [iLess0(503 ^ [_101821], 502 ^ [_101821])]], -(isTerminating0(_101821))], (483 ^ _86560) ^ [] : [isTerminating0(_101821), 486 ^ _86560 : [(487 ^ _86560) ^ [_102090, _102092] : [aElement0(_102092), aElement0(_102090), sdtmndtplgtdt0(_102092, _101821, _102090), -(iLess0(_102090, _102092))]]]]], (548 ^ _86560) ^ [] : [-(aRewritingSystem0(xR))], (576 ^ _86560) ^ [] : [-(isTerminating0(xR))], (550 ^ _86560) ^ [_104156, _104158] : [aElement0(_104158), aElement0(_104156), -(iLess0(_104156, _104158)), 559 ^ _86560 : [(560 ^ _86560) ^ [] : [aReductOfIn0(_104156, _104158, xR)], (572 ^ _86560) ^ [] : [sdtmndtplgtdt0(_104158, xR, _104156)], (562 ^ _86560) ^ [_104525] : [aElement0(_104525), aReductOfIn0(_104525, _104158, xR), sdtmndtplgtdt0(_104525, xR, _104156)]]], (515 ^ _86560) ^ [_102994, _102996] : [aElement0(_102996), aRewritingSystem0(_102994), 522 ^ _86560 : [(523 ^ _86560) ^ [_103266] : [aNormalFormOfIn0(_103266, _102996, _102994), 526 ^ _86560 : [(527 ^ _86560) ^ [] : [-(aElement0(_103266))], (529 ^ _86560) ^ [] : [-(sdtmndtasgtdt0(_102996, _102994, _103266))], (531 ^ _86560) ^ [_103542] : [aReductOfIn0(_103542, _103266, _102994)]]], (533 ^ _86560) ^ [_103617] : [-(aNormalFormOfIn0(_103617, _102996, _102994)), aElement0(_103617), sdtmndtasgtdt0(_102996, _102994, _103617), -(aReductOfIn0(542 ^ [_102994, _102996, _103617], _103617, _102994))]]]], input).
% 1.64/2.42 ncf('1',plain,[aNormalFormOfIn0(577 ^ [], 577 ^ [], xR)],start(642 ^ 0,bind([[_107389], [577 ^ []]]))).
% 1.64/2.42 ncf('1.1',plain,[-(aNormalFormOfIn0(577 ^ [], 577 ^ [], xR)), 533 : aElement0(577 ^ []), 533 : sdtmndtasgtdt0(577 ^ [], xR, 577 ^ []), 533 : -(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR)), 533 : aElement0(577 ^ []), 533 : aRewritingSystem0(xR)],extension(515 ^ 1,bind([[_102994, _102996, _103617], [xR, 577 ^ [], 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.1',plain,[-(aElement0(577 ^ []))],extension(579 ^ 4)).
% 1.64/2.42 ncf('1.1.2',plain,[-(sdtmndtasgtdt0(577 ^ [], xR, 577 ^ [])), sdtmndtasgtdt0(577 ^ [], xR, 577 ^ []), 577 ^ [] = 577 ^ [], xR = xR, 577 ^ [] = 577 ^ []],extension(102 ^ 4,bind([[_89892, _89894, _89896, _89898, _89900, _89902], [577 ^ [], 577 ^ [], xR, xR, 577 ^ [], 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.2.1',plain,[-(sdtmndtasgtdt0(577 ^ [], xR, 577 ^ [])), sdtmndtasgtdt0(577 ^ [], xR, 577 ^ []), 577 ^ [] = 577 ^ [], xR = xR, 577 ^ [] = 577 ^ []],extension(102 ^ 5,bind([[_89892, _89894, _89896, _89898, _89900, _89902], [577 ^ [], 577 ^ [], xR, xR, 577 ^ [], 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.2.1.1',plain,[-(sdtmndtasgtdt0(577 ^ [], xR, 577 ^ [])), 323 : 577 ^ [] = 577 ^ [], 321 : aElement0(577 ^ []), 321 : aRewritingSystem0(xR), 321 : aElement0(577 ^ [])],extension(299 ^ 6,bind([[_95762, _95764, _95766], [577 ^ [], xR, 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.2.1.1.1',plain,[-(577 ^ [] = 577 ^ [])],extension(2 ^ 11,bind([[_86684], [577 ^ []]]))).
% 1.64/2.42 ncf('1.1.2.1.1.2',plain,[-(aElement0(577 ^ []))],extension(579 ^ 7)).
% 1.64/2.42 ncf('1.1.2.1.1.3',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 7)).
% 1.64/2.42 ncf('1.1.2.1.1.4',plain,[-(aElement0(577 ^ []))],lemmata('[1, 2, 1, 1].x')).
% 1.64/2.42 ncf('1.1.2.1.2',plain,[-(577 ^ [] = 577 ^ [])],extension(2 ^ 6,bind([[_86684], [577 ^ []]]))).
% 1.64/2.42 ncf('1.1.2.1.3',plain,[-(xR = xR)],extension(2 ^ 6,bind([[_86684], [xR]]))).
% 1.64/2.42 ncf('1.1.2.1.4',plain,[-(577 ^ [] = 577 ^ [])],extension(2 ^ 6,bind([[_86684], [577 ^ []]]))).
% 1.64/2.42 ncf('1.1.2.2',plain,[-(577 ^ [] = 577 ^ [])],extension(2 ^ 5,bind([[_86684], [577 ^ []]]))).
% 1.64/2.42 ncf('1.1.2.3',plain,[-(xR = xR)],extension(2 ^ 5,bind([[_86684], [xR]]))).
% 1.64/2.42 ncf('1.1.2.4',plain,[-(577 ^ [] = 577 ^ [])],lemmata('[1, 1].x')).
% 1.64/2.42 ncf('1.1.3',plain,[aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR), 625 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), 625 : sdtmndtplgtdt0(542 ^ [xR, 577 ^ [], 577 ^ []], xR, 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]), 625 : aElement0(588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]), 625 : -(aReductOfIn0(638 ^ [588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]], 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], xR))],extension(615 ^ 4,bind([[_106574, _106932], [588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], 542 ^ [xR, 577 ^ [], 577 ^ []]]]))).
% 1.64/2.42 ncf('1.1.3.1',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []])), 184 : aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR), 184 : aElement0(577 ^ []), 184 : aRewritingSystem0(xR)],extension(176 ^ 7,bind([[_92177, _92179, _92399], [xR, 577 ^ [], 542 ^ [xR, 577 ^ [], 577 ^ []]]]))).
% 1.64/2.42 ncf('1.1.3.1.1',plain,[-(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR))],reduction('1.1')).
% 1.64/2.42 ncf('1.1.3.1.2',plain,[-(aElement0(577 ^ []))],lemmata('[1].x')).
% 1.64/2.42 ncf('1.1.3.1.3',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 8)).
% 1.64/2.42 ncf('1.1.3.2',plain,[-(sdtmndtplgtdt0(542 ^ [xR, 577 ^ [], 577 ^ []], xR, 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]])), 592 : -(542 ^ [xR, 577 ^ [], 577 ^ []] = 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]), 592 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), 592 : iLess0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [])],extension(581 ^ 7,bind([[_105350], [542 ^ [xR, 577 ^ [], 577 ^ []]]]))).
% 1.64/2.42 ncf('1.1.3.2.1',plain,[542 ^ [xR, 577 ^ [], 577 ^ []] = 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], -(aReductOfIn0(638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], xR)), aReductOfIn0(638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], 542 ^ [xR, 577 ^ [], 577 ^ []], xR), 638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]] = 638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], xR = xR],extension(120 ^ 10,bind([[_90501, _90503, _90505, _90507, _90509, _90511], [xR, xR, 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], 542 ^ [xR, 577 ^ [], 577 ^ []], 638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], 638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]]]))).
% 1.64/2.42 ncf('1.1.3.2.1.1',plain,[aReductOfIn0(638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], xR)],extension(611 ^ 11,bind([[_106402], [638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]]]))).
% 1.64/2.42 ncf('1.1.3.2.1.2',plain,[-(aReductOfIn0(638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], 542 ^ [xR, 577 ^ [], 577 ^ []], xR)), aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), 623 : aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR)],extension(615 ^ 11,bind([[_106574], [542 ^ [xR, 577 ^ [], 577 ^ []]]]))).
% 1.64/2.42 ncf('1.1.3.2.1.2.1',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[1, 1].x')).
% 1.64/2.42 ncf('1.1.3.2.1.2.2',plain,[-(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR))],reduction('1.1')).
% 1.64/2.42 ncf('1.1.3.2.1.3',plain,[-(638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]] = 638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]])],extension(2 ^ 11,bind([[_86684], [638 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]]]))).
% 1.64/2.42 ncf('1.1.3.2.1.4',plain,[-(xR = xR)],extension(2 ^ 11,bind([[_86684], [xR]]))).
% 1.64/2.42 ncf('1.1.3.2.2',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[1, 1].x')).
% 1.64/2.42 ncf('1.1.3.2.3',plain,[-(iLess0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [])), 487 : aElement0(577 ^ []), 487 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), 487 : sdtmndtplgtdt0(577 ^ [], xR, 542 ^ [xR, 577 ^ [], 577 ^ []]), 487 : isTerminating0(xR), 483 : aRewritingSystem0(xR)],extension(479 ^ 8,bind([[_101821, _102090, _102092], [xR, 542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.3.2.3.1',plain,[-(aElement0(577 ^ []))],lemmata('[1].x')).
% 1.64/2.42 ncf('1.1.3.2.3.2',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.2.3.3',plain,[-(sdtmndtplgtdt0(577 ^ [], xR, 542 ^ [xR, 577 ^ [], 577 ^ []])), 259 : aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR), 257 : aElement0(577 ^ []), 257 : aRewritingSystem0(xR), 257 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []])],extension(230 ^ 13,bind([[_93687, _93689, _93691], [542 ^ [xR, 577 ^ [], 577 ^ []], xR, 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.3.2.3.3.1',plain,[-(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR))],reduction('1.1')).
% 1.64/2.42 ncf('1.1.3.2.3.3.2',plain,[-(aElement0(577 ^ []))],lemmata('[2, 3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.2.3.3.3',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 14)).
% 1.64/2.42 ncf('1.1.3.2.3.3.4',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[2, 3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.2.3.4',plain,[-(isTerminating0(xR))],extension(576 ^ 11)).
% 1.64/2.42 ncf('1.1.3.2.3.5',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 9)).
% 1.64/2.42 ncf('1.1.3.3',plain,[-(aElement0(588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]])), aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), iLess0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [])],extension(581 ^ 5,bind([[_105350], [542 ^ [xR, 577 ^ [], 577 ^ []]]]))).
% 1.64/2.42 ncf('1.1.3.3.1',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []])), 184 : aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR), 184 : aElement0(577 ^ []), 184 : aRewritingSystem0(xR)],extension(176 ^ 6,bind([[_92177, _92179, _92399], [xR, 577 ^ [], 542 ^ [xR, 577 ^ [], 577 ^ []]]]))).
% 1.64/2.42 ncf('1.1.3.3.1.1',plain,[-(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR))],reduction('1.1')).
% 1.64/2.42 ncf('1.1.3.3.1.2',plain,[-(aElement0(577 ^ []))],lemmata('[1].x')).
% 1.64/2.42 ncf('1.1.3.3.1.3',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 7)).
% 1.64/2.42 ncf('1.1.3.3.2',plain,[-(iLess0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [])), 487 : aElement0(577 ^ []), 487 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), 487 : sdtmndtplgtdt0(577 ^ [], xR, 542 ^ [xR, 577 ^ [], 577 ^ []]), 487 : isTerminating0(xR), 483 : aRewritingSystem0(xR)],extension(479 ^ 6,bind([[_101821, _102090, _102092], [xR, 542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.3.3.2.1',plain,[-(aElement0(577 ^ []))],lemmata('[1].x')).
% 1.64/2.42 ncf('1.1.3.3.2.2',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.3.2.3',plain,[-(sdtmndtplgtdt0(577 ^ [], xR, 542 ^ [xR, 577 ^ [], 577 ^ []])), 259 : aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR), 257 : aElement0(577 ^ []), 257 : aRewritingSystem0(xR), 257 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []])],extension(230 ^ 11,bind([[_93687, _93689, _93691], [542 ^ [xR, 577 ^ [], 577 ^ []], xR, 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.3.3.2.3.1',plain,[-(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR))],reduction('1.1')).
% 1.64/2.42 ncf('1.1.3.3.2.3.2',plain,[-(aElement0(577 ^ []))],lemmata('[3, 3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.3.2.3.3',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 12)).
% 1.64/2.42 ncf('1.1.3.3.2.3.4',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[3, 3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.3.2.4',plain,[-(isTerminating0(xR))],extension(576 ^ 9)).
% 1.64/2.42 ncf('1.1.3.3.2.5',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 7)).
% 1.64/2.42 ncf('1.1.3.4',plain,[aReductOfIn0(638 ^ [588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]], 588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]], xR), aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), iLess0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [])],extension(581 ^ 5,bind([[_105350, _106402], [542 ^ [xR, 577 ^ [], 577 ^ []], 638 ^ [588 ^ [542 ^ [xR, 577 ^ [], 577 ^ []]]]]]))).
% 1.64/2.42 ncf('1.1.3.4.1',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []])), 184 : aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR), 184 : aElement0(577 ^ []), 184 : aRewritingSystem0(xR)],extension(176 ^ 6,bind([[_92177, _92179, _92399], [xR, 577 ^ [], 542 ^ [xR, 577 ^ [], 577 ^ []]]]))).
% 1.64/2.42 ncf('1.1.3.4.1.1',plain,[-(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR))],reduction('1.1')).
% 1.64/2.42 ncf('1.1.3.4.1.2',plain,[-(aElement0(577 ^ []))],lemmata('[1].x')).
% 1.64/2.42 ncf('1.1.3.4.1.3',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 7)).
% 1.64/2.42 ncf('1.1.3.4.2',plain,[-(iLess0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [])), 487 : aElement0(577 ^ []), 487 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]), 487 : sdtmndtplgtdt0(577 ^ [], xR, 542 ^ [xR, 577 ^ [], 577 ^ []]), 487 : isTerminating0(xR), 483 : aRewritingSystem0(xR)],extension(479 ^ 6,bind([[_101821, _102090, _102092], [xR, 542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.3.4.2.1',plain,[-(aElement0(577 ^ []))],lemmata('[1].x')).
% 1.64/2.42 ncf('1.1.3.4.2.2',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.4.2.3',plain,[-(sdtmndtplgtdt0(577 ^ [], xR, 542 ^ [xR, 577 ^ [], 577 ^ []])), 259 : aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR), 257 : aElement0(577 ^ []), 257 : aRewritingSystem0(xR), 257 : aElement0(542 ^ [xR, 577 ^ [], 577 ^ []])],extension(230 ^ 11,bind([[_93687, _93689, _93691], [542 ^ [xR, 577 ^ [], 577 ^ []], xR, 577 ^ []]]))).
% 1.64/2.42 ncf('1.1.3.4.2.3.1',plain,[-(aReductOfIn0(542 ^ [xR, 577 ^ [], 577 ^ []], 577 ^ [], xR))],reduction('1.1')).
% 1.64/2.42 ncf('1.1.3.4.2.3.2',plain,[-(aElement0(577 ^ []))],lemmata('[4, 3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.4.2.3.3',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 12)).
% 1.64/2.42 ncf('1.1.3.4.2.3.4',plain,[-(aElement0(542 ^ [xR, 577 ^ [], 577 ^ []]))],lemmata('[4, 3, 1, 1].x')).
% 1.64/2.42 ncf('1.1.3.4.2.4',plain,[-(isTerminating0(xR))],extension(576 ^ 9)).
% 1.64/2.42 ncf('1.1.3.4.2.5',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 7)).
% 1.64/2.42 ncf('1.1.4',plain,[-(aElement0(577 ^ []))],extension(579 ^ 2)).
% 1.64/2.42 ncf('1.1.5',plain,[-(aRewritingSystem0(xR))],extension(548 ^ 2)).
% 1.64/2.42 %-----------------------------------------------------
% 1.64/2.42 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------